Minimizing one variable function with different parameters, time-efficient solution

Hello,

I want to minimize a one variable function f(x) for different values of one parameter a. I found this solution:

function y=f(x,a)
y=abs(phi(x))+(x-a).^2; % phi is a differentiable function
end
-----------------
eps=0.2 
for i=1:size(a,1)
xmin=fminbnd(@(x)f(x,a(i)),a(i)-eps,a(i)+eps); % we know the minimum is close to a
end

Vector a has more than 450000 values, so it takes an unacceptable computation time. Do you think there exists another more time-efficient solution?

Thank you in advance

[Babak]

Are you looking to find xmin which is the same size as a?

In other words, xmin in your for loop is over-writing itself.

My understanding from your question is that you are looking for a curve of xmin(a) that for different values of a, gives you minimum values of the function g(x) = f(x,a). Am I right?

Answer 1

[Matt J]

Do you expect xmin(i) to be close to xmin(i-1)? If so, you could do

eps=0.2;
xmin=nan(size(a)); %pre-allocate

xmin(1)=fminbnd(@(x)f(x,a(1)),a(1)-eps,a(1)+eps);  %initialize

for i=2:size(a,1)
 xmin(i)=fminsearch(@(x)f(x,a(i)),xmin(i-1)); 
end